Ministry of Education and Science of the Russian Federation.

Federal Agency for Education.

State educational institution of higher professional education.

Samara State Technical University.

Department: "Applied Mechanics"

Course project in mechanics

Student 2 - HT - 2

Head: Ph.D., Associate Professor

Terms of Reference No. 65.

Bevel gear.

Motor shaft speed:

.

Torque on the output shaft of the gearbox:

.

Output shaft speed:

.

Reducer service life in years:

.

Gearbox load factor during the year:

.

Gearbox load factor during the day:

.

1. Introduction _______________________________________________________________4

2. Kinematic and power calculation of the drive ________________________________4

2.1 Determining the speed of the gearbox shafts ______________________ 4

2.2. Calculation of the number of teeth of the wheels ______________________________________________4

2.3. Determination of the actual gear ratio _______________5

2.4. Determination of the efficiency of the gearbox ___________________________________________5

2.5. Determination of rated load torques on each shaft, mechanism diagram ______________________________________________________________5

2.6. Calculation of the required power and the choice of the electric motor, its dimensions ___5

3. Selection of materials and calculation of allowable stresses_________________7

3.1. Determination of the hardness of materials, selection of material for the gear

3.2. Calculation of allowable stresses _________________________________7

3.3. Permissible stresses for contact endurance ______________ 7

3.4. Permissible stresses for bending endurance ________________8

4. Design and verification calculation of transmission ________________________________8

4.1. Calculation of the preliminary pitch diameter of the gear ______8

4.2. Calculation of the preliminary transmission module and its refinement in accordance with GOST ___________________________________________________________8

4.3. Calculation of the geometric parameters of transmission ____________________________________8

4.4. Transmission check calculation ________________________________________________ 9

4.5. Efforts in gearing ___________________________________________ 9

5. Design calculation of the shaft and the choice of bearings ______________________ 12

6. Sketch layout and calculation of structural elements _______________12

6.1. Gear wheel calculation

6.2. Calculation of hull elements ____________________________________________13

6.3. Calculation of oil-retaining rings _________________________________13

6.4. Bearing cap calculation __________________________________13

6.5. Execution of the layout drawing ________________________________13

7. Selection and verification calculation of keyed connections _______________14

8. Verification calculation of the shaft for fatigue endurance ______________ 15

9. Verification calculation of output shaft bearings for durability___18

10. Selection and calculation of the coupling _________________________________19

11. Gearbox lubrication __________________________________________19

12. Assembly and adjustment of the main components of the gearbox ___________________20

13. List of used literature ________________________________22

14. Applications__________________________________________________23

Introduction.

A gearbox is a mechanism consisting of gears or worm gears, made in the form of a separate unit and serving to transfer rotation from the motor shaft to the shaft of the working machine.

The purpose of the gearbox is to reduce the angular velocity and, accordingly, increase the torque of the driven shaft compared to the driving one.

The gearbox consists of a housing (cast iron or welded steel), in which the transmission elements are placed - gears, shafts, bearings, etc. In some cases, devices for lubricating gears and bearings or devices for cooling are also placed in the gearbox housing.

Reducers are classified according to the following main features: type of transmission (gear, worm or gear-worm); number of stages (single-stage, two-stage, etc.); type of gears (cylindrical, bevel, bevel-cylindrical, etc.); the relative arrangement of the gearbox shafts in space (horizontal, vertical); features of the kinematic scheme (deployed, coaxial, with a forked step, etc.).

Bevel gearboxes are used to transmit motion between shafts, the axes of which usually intersect at an angle of 90. Gears with angles other than 90 are rare.

The most common type of bevel gearbox is a gearbox with a vertically located low-speed shaft. Execution of a reducer with vertically located high-speed shaft is possible; in this case, the drive is carried out from a flange motor

The gear ratio u of single-stage bevel gears with spur gears, as a rule, is not higher than 3; in rare cases, u = 4. With oblique or curved teeth, u = 5 (as an exception, u = 6.3).

For gear units with bevel spur gears, the permissible circumferential speed (along the pitch circle of the average diameter) is v ≤ 5 m/s. At higher speeds, it is recommended to use bevel gears with circular teeth, which provide smoother engagement and greater load-bearing capacity.

2 Kinematic and power calculation of the drive.

2.1 Determining the speed of the gearbox shafts:

.

Speed ​​of rotation of the first (input) shaft:

.

The frequency of rotation of the second (output) shaft:

.

2.2 Calculation of the number of gear teeth.

Estimated number of gear teeth

determined depending on the value of the gear ratio of the transmission:

Meaning

rounded up to a whole number according to the rules of mathematics: .

Estimated number of teeth of the wheel

, necessary for the implementation of the gear ratio, is determined by the dependence: .

Meaning

rounded up to a whole number: .

2.3 Determination of the actual gear ratio:

.

2.4 Determination of the efficiency of the gearbox.

For bevel gear

.

Torque (load) moment on the gearbox output shaft:

.

On the input shaft:

.

2.5 Determination of rated load torques on each shaft, mechanism diagram.

Power on the output shaft of the gearbox, kW:

kW , where: - output shaft torque, - output shaft speed.

Estimated power of the electric motor.

IRKUTSK STATE TECHNICAL UNIVERSITY

Department of Design and Standardization in Mechanical Engineering

Theory of machines and mechanisms

Methodical instructions and tasks for the section:

"Determination of the gear ratio in multi-stage gears"

Irkutsk 2007

Theory of machines and mechanisms. Guidelines and tasks for the section: "Determination of the gear ratio in multi-stage gears." Shmatkova A.V. - Irkutsk: Publishing house of ISTU. - 2007. -20 p.

This guideline is intended for students studying the course "Theory of Machines and Mechanisms".

Reviewer:

Signed for printing 20.01.07 Format 60х84 1/16

Printing paper. Offset printing, conv. print sheet 1.25. Uch-ed. l. 1.35

Circulation 200 copies. S-20.

Irkutsk State Technical University

664074, Irkutsk, st. Lermontov, 83

Foreword

This guideline is intended for students studying the course "Theory of Machines and Mechanisms".

In this course, students should learn the basic methods of calculating and analyzing various schemes of mechanisms.

This guideline provides tasks and discusses some issues of solving problems to determine the gear ratio in multi-stage gears.

EXERCISE

Determine the gear ratio of the mechanism and the speed of rotation of the output shaft. The missing number of teeth of the wheels is determined from the condition of alignment, assuming that all wheels have the same module and engagement angle. Design schemes are shown in Figures 1.1 - 1.32, the initial data in Table 1.

THEORY

The gear ratio of wheel 1 to wheel 2 is the ratio of the angular velocity (or rpm) of link 1 to the angular velocity (or) of link 2:

.

Thus:

The gear ratio is assigned a minus sign for external gearing of the wheels, a plus sign for internal gearing. The sign of the gear ratio indicates the direction of rotation of the driven link in relation to the leading link.

The gear ratio of a mechanism consisting of k steps is determined by the formula: ,

where n is the number of external links.

For planetary mechanisms, the gear ratio is determined by the formula (table 2): ,

where is the input link, is the output link (carrier), is the fixed link.

If the input link in the planetary mechanism is the carrier, then the calculation of the gear ratio should begin with the following formula:.

option number	Scheme Fig. No.	n 1 (n H1)	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8	Z9	Z10	Z11	Z12	Z13	Z14	Z15
	1.1	1000	30	20	25	-	25	50	-	40	15	20	25	45	-	-	-
	1.2	2000	15	30	45	40	20	-	17	34	40	25	22	26	-	-	-
	1.3	1500	-	18	20	47	21	23	31	45	30	30	45	-	-	-	-
	1.4	3000	40	30	10	70	20	15	-	30	35	60	12	21	18	30	25
	1.5	2500	25	35	-	15	-	40	30	20	10	25	20	10	30	-	-
	1.6	1000	30	15	22	18	24	22	40	10	20	-	35	15	-	-	-
	1.7	2000	40	15	-	12	24	18	54	30	18	15	-	30	25	17	15
	1.8	1500	50	27	32	35	10	14	30	25	17	19	10	40	-	25	30
	1.9	3000	17	34	17	30	25	25	30	50	18	17	34	18	-	-	-
	1.10	2500	18	33	22	17	32	60	20	17	-	-	17	30	20	18	36
	1.11	1000	21	17	17	30	19	-	20	20	-	25	19	17	30	42	34
	1.12	2000	18	33	27	70	19	20	-	17	34	-	40	20	40	18	30
	1.13	1500	17	34	36	20	18	-	17	17	34	31	17	19	31	-	-
	1.14	3000	18	36	17	68	34	18	24	-	38	18	40	20	29	-	-
	1.15	2500	17	27	17	17	34	17	51	78	20	-	68	32	19	22	-
	1.16	1000	15	20	17	40	60	22	25	-	-	17	21	40	15	30	-
	1.17	2000	15	12	19	30	31	-	30	15	25	15	20	15	15	-	-
	1.18	4000	15	30	15	-	70	50	14	28	14	25	30	17	33	17	-
	1.19	1500	20	30	27	17	-	34	17	17	-	22	18	24	32	34	-
	1.20	3000	40	20	25	30	32	22	17	-	17	19	24	-	17	-	34
	1.21	1000	60	20	18	24	16	-	17	18	31	19	18	30	-	-	-
	1.22	2500	18	20	40	20	-	80	30	25	30	29	20	22	24	25	30
	1.23	4000	80	18	-	70	40	17	20	40	19	37	20	30	40	-	-
	1.24	2000	20	18	17	29	17	19	30	25	40	20	35	18	18	40	-
	1.25	3000	30	25	30	20	40	17	-	20	17	17	-	19	51	17	-
	1.26	1000	18	19	33	28	17	51	30	25	17	34	17	34	30	18	-
	1.27	2000	20	18	34	17	21	-	22	24	40	18	-	24	22	18	-
	1.28	1000	70	22	20	-	30	25	-	35	25	20	-	30	25	40	-
	1.29	4000	36	18	24	-	17	34	28	22	26	19	17	26	17	19	18
	1.30	2500	80	40	-	60	30	18	-	28	19	32	24	26	40	-	20
	1.31	1000	17	29	31	17	30	27	30	20	20	-	40	30	17	34	-
	1.32	2000	30	28	25	18	33	40	20	18	18	-	30	17	19	18	-

Table 1

		Fig.1.12.

	Fig.1.17.
	Fig.1.18.

	Fig.1.19.

PROCEDURE

1. From the condition of alignment, determine the missing number of teeth of the wheels.

2. Break the mechanism into separate steps.

3. Determine the gear ratio of each stage.

4. Determine the gear ratio of the mechanism as a whole as the product of the gear ratios of individual steps.

The required drive power is determined by the formula:

where T 2 – moment on the output shaft (Nm);

n 2 - frequency of rotation of the output shaft (rpm).

Determination of the required power of the electric motor.

The required motor power is determined by the formula

where η gearbox- efficiency of the gearbox;

According to the kinematic scheme of a given drive, the efficiency of the gearbox is determined by the dependence:

η gearbox = η engagement η 2 bearings η couplings ,

where η engagement– gearing efficiency; accept η engagement = 0,97 ;

η bearings– efficiency of a pair of rolling bearings; accept η bearings = 0,99 ;

η couplings– clutch efficiency; accept η couplings = 0,98 .

1.3. Determination of the frequency of rotation of the motor shaft.

We determine the speed range in which the synchronous speed of the electric motor can be located by the formula:

n with = un 2 ,

where u- gear ratio of the stage; we select the range of gear ratios, which is recommended for one stage of a spur gear in the range from 2 - 5.

for example: n with = un 2 = (2 - 5)200 = 400 - 1000 rpm.

1.4. Motor selection.

According to the required power of the electric motor R cons.(given that R el.dv. ≥ R cons.) and synchronous shaft speed n with choose an electric motor:

series…..

power R= ……kW

synchronous speed n with= …..rpm

asynchronous speed n 1 = …..r/min.

Rice. 1. Sketch of the electric motor.

1.5. Determination of the gear ratio of the gearbox.

According to the calculated value of the gear ratio, we select the standard value, taking into account the error, from a series of gear ratios. Accept u Art. = ….. .

1.6. Determination, speeds and torques on the shafts of the gearbox.

Input shaft speed n 1 = ….. rpm.

Output shaft speed n 2 = ….. rpm.

Torque on the output shaft wheel:

Torque on the input shaft gear:

2. CALCULATION OF A CLOSED GEAR.

2.1. Design calculation.

1. Choice of wheel material.

for example:

Gear Wheel

HB = 269…302 HB = 235…262

HB 1 = 285 HB 2 = 250

2. We determine the allowable voltage contacts for the gear teeth and wheels :

where  H lim - endurance limit of the contact surface of the teeth, corresponding to the basic number of cycles of alternating stresses; determined depending on the hardness of the tooth surface or a numerical value is set;

for example:  H lim = 2HB+70.

S H– safety factor; for gears with uniform material structure and tooth surface hardness HB 350 recommended S H = 1,1 ;

Z N– durability coefficient; for gears during long-term operation with a constant load mode, it is recommended Z N = 1 .

Finally, the smaller of the two values ​​of the allowable contact stresses of the wheel and gear is taken as the allowable contact stress [  H] 2 and [  H ] 1:[ H ] = [ H ] 2 .

3. Determine the center distance from the condition of contact endurance of the active surfaces of the teeth .

where E etc- reduced modulus of elasticity of wheel materials; for steel wheels can be accepted E etc= 210 5 MPa;

 ba- coefficient of wheel width relative to the center distance; for wheels located symmetrically with respect to the supports, it is recommended ψ ba = 0,2 – 0,4 ;

To H  is the load concentration factor in calculations for contact stresses.

To determine the coefficient To H  it is necessary to determine the ratio of the relative width of the ring gear relative to the diameter ψ bd : ψ bd = 0,5ψ ba (u1)=….. .

According to the graph of the figure ... .. taking into account the location of the gear relative to the supports, with hardness HB 350, according to the value of the coefficient ψ bd we find: To H  = ….. .

We calculate the center distance:

for example:

For gearboxes, the center distance is rounded off according to a series of standard center distances or a series Ra 40 .

Assign a W= 120 mm.

4. Determine the transmission module.

m = (0,01 – 0,02)a W= (0.01 - 0.02)120 = 1.2 - 2.4 mm.

For a number of modules from the obtained interval, we assign the standard value of the module: m= 2 mm.

5. Determine the number of gear teeth and wheels.

The total number of teeth of the gear and wheel is determined from the formula: a W = m(z 1 +z 2 )/2;

from here z   = 2a W /m= …..; accept z  = ….. .

Number of gear teeth: z  1 = z  /(u1) = …..

To eliminate undercut teeth z 1 ≥ z min ; for spur engagement z min = 17 . Accept z 1 = ….. .

Number of wheel teeth: z 2 = z  - z 1 = .. Recommended z 2  100 .

6. We specify the gear ratio.

We determine the actual gear ratio by the formula:

The error in the value of the actual gear ratio from the calculated value:

The design accuracy condition is met.

For the gear ratio of the gearbox, we take u fact = ….. .

7. We determine the main geometric dimensions of the gear and wheel.

For wheels cut without tool offset:

pitch circle diameters

d W = d

engagement angle and profile angle

α W = α = 20º

pitch diameters

d 1 = z 1 m

d 2 = z 2 m

tooth tip diameters

d a1 = d 1 +2 m

d a2 = d 2 +2 m

cavity diameters

d f 1 = d 1 –2,5 m

d f 2 = d 2 –2,5 m

tooth height

h = 2,25 m

ring gear width

b w = ψ ba a W

gear and wheel ring width

b 2 = b w

b 1 = b 2 + (3 - 5) = ..... . Accept b 1 = ….. mm.

check the value of the center distance

a w = 0,5  (d 1 + d 2 )

INTRODUCTION

Worm gear refers to gears with intersecting shafts.

The main advantages of worm gears: the possibility of obtaining large gear ratios in one pair, smooth engagement, the possibility of self-braking. Disadvantages: relatively low efficiency, increased wear and a tendency to seize, the need to use expensive anti-friction materials for wheels.

Worm gears are more expensive and more complicated than gears, so they are used, as a rule, when it is necessary to transfer motion between intersecting shafts, and also where a large gear ratio is needed.

The criterion for the performance of worm gears is the surface strength of the teeth, which ensures their wear resistance and the absence of chipping and seizing, as well as bending strength. Under the action of short-term overloads in the worm gear, the teeth of the worm wheel are checked for bending according to the maximum load.

For the body of the worm, a verification calculation for stiffness is carried out, and a thermal calculation is also carried out.

The design is carried out in two stages: design - from the conditions of contact endurance, the main dimensions of the transmission are determined and verification - with known parameters of the transmission under the conditions of its operation, contact and bending stresses are determined and compared with those allowed by the endurance of the material.

The forces loading the bearings are determined and the bearings are selected according to their load capacity.

KINEMATIC AND FORCE CALCULATION

Motor selection

To select an electric motor, its required power and speed are determined.

According to the initial design data, the required power to perform the technological process can be found from the formula:

P out \u003d F t V, (2.1)

where P out - power on the output shaft of the drive, W;

F t - traction force, N;

V is the speed of movement of the working body, m/s;

P out \u003d 1.5 kW.

Determination of the overall efficiency drive

Then, in accordance with the kinematic power transmission chain, the total efficiency. of the entire drive is calculated by the formula:

s total = s 1 s 2 s 3 s 4 (2.2)

h total = 0.80.950.980.99 = 0.74.

Thus, based on the overall efficiency. it became clear that during the operation of the drive, only 74% of the power from the engine would go to the winch drum.

Let's determine the required engine power for normal operation of the winch:

We accept a 2.2 kW motor.

Calculation of the rotational speed of the motor shaft

Since at this stage the gear ratios of the drive gears are still unknown and the motor shaft speed is not known, it becomes possible to calculate the desired speed of the motor shaft.

For this, the following calculations were carried out.

Determination of the speed of the output shaft of the drive

According to the initial data, the angular velocity of the output shaft is calculated by the formula:

where u - angular velocity, s -1;

D b - drum diameter, m;

v is the speed of movement of the working body, m/s.

Let's find the rotation frequency, knowing the angular velocity by the formula:

rpm (2.5)

Determining the desired drive ratio

From the analysis of the kinematic diagram of the electric winch drive, it can be seen that its total gear ratio (u total) is formed due to the gear ratio of the worm gear reducer.

We accept u chp = 50. The relationship between the frequencies of rotation of the motor shaft n dv and the output shaft n z is determined by the relationship:

n dv = n z u total, (2.6)

then the desired speed of the motor shaft will be:

n engine = 38.250 = 1910 rpm.

According to the current range of motors, the one closest to the desired speed is a motor with a synchronous speed of 1500 rpm. In view of the foregoing, we finally accept the brand engine: 90L4 / 1395. AIR series, which has the following characteristics:

R dv \u003d 2.2 kW;

n motor = 1500 rpm.

Kinematic calculations

Total gear ratio:

u total \u003d n dv / \u003d 1500 / 38.2 \u003d 39.3.

Let us determine all the kinematic characteristics of the designed drive, which will be needed in the future for a detailed study of the transmission. Determination of frequency and rotation speeds. It is easy to calculate the rotational speeds of all shafts, starting from the selected rotational speed of the electric motor shaft, taking into account the fact that the rotational speed of each subsequent shaft is determined through the rotational speed of the previous one according to the formula (2.7), taking into account the gear ratio:

where n (i+1) - speed i+1 shaft, rpm;

u i -(i+1) - gear ratio between i and i+1 shafts.

Moments on the gearbox shafts:

T 1 \u003d 9.5510 3 (P / n e) \u003d 9.5510 3 (2.2 / 1500) \u003d 14.0 Nm

T 2 \u003d T 1 u \u003d 14.039.3 \u003d 550 Nm.