Worm Wheel Design Process

Worm Gearing The calculation is used for geometrical and strength designs and worm gearing check. The program solves the following tasks. 1. Calculation of gearing dimensions. 2. Automatic transmission design with minimum input requirements. 3. Design for safety coefficients entered. 4. Calculation of a table of proper solutions. 5. Calculation of complete geometrical parameters. 6. Calculation of strength parameters, safety check. 7. Gearing design for precise centre-line distance. 8. Auxiliary calculations (heating, shaft design). 9. Support of 2D and 3D CAD systems. The calculations use procedures, algorithms and data from standards ANSI, ISO, DIN, BS and specialized literature. List of standards: ANSI/AGMA 6022-C93 (Revision of AGMA 341.02), ANSI/AGMA 6034-B92 (Revision of ANSI/AGMA 6034-A87), DIN 3996, DIN 3975-1, DIN 3975-2 Hint: The comparative document Choices of transmission can be helpful when selecting a suitable transmission type.

Control, structure and syntax of calculations. Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

Information on the project. Information on the purpose, use and control of the paragraph "Information on the project" can be found in the document "Information on the project".

Theory Application Worm (globoid) gearing can transmit high outputs, the common ones being 50 to 100 kW (optimum 0.04kW-120kW, extreme 1000 kW); within one stage, it is able to realize high transmission ratios i = 5 to 100, (up to i=1000 in kinematical transmissions), being of small size, low weight, and compact structure. It features quiet and silent operation and can be designed as a self-locking transmission. The disadvantage is the large slip in the gearing causing higher friction losses and thereby lower transmission efficiency; the endeavours for improvement require using deficit nonferrous metals for wormgear rims. Gearing production is more demanding and expensive and the service life of such gearing is usually shorter than in rolling gearing. Worm gearing is used for power transmission in mixers, vertical lathes, vehicles and lifting equipment, textile machines, presses, conveyors, shears, drums, hoists, ship propeller drives, planers, machine tools, cars... This calculation deals with the most frequently used gearing with cylindrical worm and globoid gear. Geometry

Worm gearing is a special case of screw gearing with the angle of axes 90° and a low number of pinion/worm teeth (mostly z1=1-4). Worm gearing types are distinguished by shape as follows: 1. Cylindrical wheel/cylindrical worm (kinematical, non-power transmissions, low torque, manual drive, adjusting mechanisms, point contact of teeth, cheap production) 2. Cylindrical worm/globoid wheel – most frequent (power transmissions, compact design, divided by cylindrical worm shape – see below) 3. Globoid worm/cylindrical wheel (not used) 4. Globoid wheel and worm (high outputs, compact design, special production, highest quality, high price)

Types of cylindrical worms:  ZA – wormgear with straight-line (trapezoidal) tooth profile in axial section; the tooth sides are slightly convex in the normal section; the cross section results in the spiral of Archimedes. The elements in the axial section are usually standardized, i.e. mx=m, x=. The gearing is produced using lathes or thread-cutting machines (the worm resembles a motion screw with trapezoidal threads). A tool shaped as the basic profile is applied onto the

workpiece in the axial plane. With larger  angles, different cutting angles occur in the forming tool on the lateral edges, which results in unequal cutting edge loading and blunting. The lateral worm areas can only be sharpened using a special form grinding wheel. Therefore, spiral gearing is used in worms with a low pitch angle (4; the worm resembles a cylindrical gear with helical teeth. Tooth sides can be ground with the flat side of the grinding wheel; special grinding machines must be used given the relatively small angle . 

ZK – profile formed by a cone ground using a wheel and/or shank tool



ZH – concave tooth profile (the most perfect and most expensive)

Note: The worm type options depend particularly on the production possibilities and transmission used. Detailed information is available in professional and the firm’s literature. Formulas (geometry calculation) The formulas given in this article are used in geometry calculation.

1- Centre-line section (mx,x,sx,ex) , 2-Normal section (mn,n,sn,en), 3-Worm frontal section Worm basic profile parameters: m (DP for calculation in inches),,ha*,c*,rf* Module and pressure angle in the centre-line section are selected for spiral gearing ZA, while module and pressure angle in the normal section are selected for common gearing ZN,ZI,ZK,ZH. Worm and worm gear parameters: z1, z2, x1=0, x2=x 1. Transmission ratio i=z1 / z2 2. Pitch diameter

ZA: d1=mx • z1 / tan() = q • mx; d2=mx • z2 ZN: d1=mn • z1 / tan() = q • mn; d2=mn • z2

3. Rolling diameter ZA: dw1=d1+2 • x • mx; dw2=d2 ZN: dw1=d1+2 • x • mn; dw2=d2 4. Equivalent diameter: dwe2=2 • a - d2 5. Mean diameter: DIN (10): dm1=2 • a - dm2; (11) dm1=q • mx

6. Tip diameter ZA: da1=d1 + 2 • ha* • mx; da2=d2 + 2 • (ha* + x) • mx; dae2 = da2 + 2 • v • mx ZN: da1=d1 + 2 • ha* • mn; da2=d2 + 2 • (ha* + x) • mn; dae2 = da2 + 2 • v • mn 7. Root diameter ZA: df1=d1 - 2 • (ha* + c*) • mx; df2=d2 - 2 • (ha* + c* - x) • mx ZN: df1=d1 - 2 • (ha* + c*) • mn; df2=d2 - 2 • (ha* + c* - x) • mn 8. Addendum ZA: ha1=ha* • mx; ha2=(ha* + x) • mx ZN: ha1=ha* • mn; ha2=(ha* + x) • mn 9. Dedendum ZA: hf1=(ha* + c*) • mx; hf2=(ha* + c* - x) • mx ZN: hf1=(ha* + c*) • mn; hf2=(ha* + c* - x) • mn 10. Pitch angle

ZA: tan()=mx • z1 / d1 = z1 / q ZN: tan()=mx • z1 / d1 = z1 / q

11. Tooth thickness; Tooth space thickness

 • mx; sn1=en1=0.5 •  • mx • cos();  • mx + 2 • x • mx • tan(x); ex2=0.5 •  • mx - 2 • x • mx • tan(x); sn2=sx2 • cos(); en2=ex2 • cos() ZN: sn1=en1=0.5 •  • mn; sx1=ex1=0.5 •  • mn / cos() sn2=0.5 •  • mn + 2 • x • mn • tan(n); en2=0.5 •  • mn - 2 • x • mn • tan(n); sx2=sn2 / cos(); ex2=en2 / cos() ZA: sx1=ex1=0.5 • sx2=0.5 •

12. Worm face width ČSN(ZA): [z1=4] L=(11 + 0.09 • z2) • mx ČSN(ZN): [z1=4] L=(11 + 0.09 • z2) • mn DIN (40): L=((de2 / 2)^2 -(a - da1 / 2)^2)^0.5 13. Worm gear face width ČSN: [z1=4] b2=0.67 • (1 + 2 / q) • d1 DIN: b25

0 - 10

-10 - 0

110 … 130

110 … 130

110 … 130

0 - 10

>0

110 … 150

110 … 150

110 … 150

10 - 30

>0

200 … 245

150 … 200

150 … 200

30 - 55

>0

350 … 510

245 … 350

200 … 245

55 - 80

>0

510 … 780

350 … 510

245 … 350

80 - 100

>0

900 … 1100

510 … 780

350 … 510

AGMA-ISO comparison table AGMA no of Gear Oil R&O

EP

ISO Viscosity Grade

1

VG 46

2

2 EP

VG 68

3

3 EP

VG 100

4

4 EP

VG 150

5

5 EP

VG 220

6

6 EP

VG 320

7 7comp

7 EP

VG 460

8 8comp

8 EP

VG 680

8A comp 9

VG 1000 9 EP

VG 1500

2.9 Kinematical viscosity for 40°C and 100°C Enter the value from the oil manufacturer’s material sheet. 2.10 Lubricant density at 15°C Enter the value from the oil manufacturer’s material sheet. 2.11 Roughness average value of the worm Enter the roughness value. The following Ra values can be achieved for working methods: 

Milling: common Ra=1.6-6.3 m (63-250inch); under special conditions up to 0.2m (8inch)



Machining: common Ra=0.8-6.3 m (32-250inch); under special conditions up to 0.1m (4inch)



Grinding: common Ra=0.2-1.6 m (8-63inch); under special conditions up to 0.05m (2inch)

2.12 Application factor It is proposed based on load irregularity from the driven/driving machine [2.4,2.5]. The value is filled in automatically after activating the ticking box. The KA factor is used to multiply the torque value. 2.13 Desired service life The parameter specifies the desired service life in hours. Orientation values in hours are given in the table. Specification

Durability

Household machines, seldom used devices

2000

Electric hand tools, machines for short-term runs

5000

Machines for 8-hour operation

20000

Machines for 16-hour operation

40000

Machines for continuous operation

80000

Machines for continuous operation with log service life

150000

2.14 Requested coefficients of safety Use lines [2.14-2.17] to enter the requested coefficients of safety. When calculating the table of proper solutions [4.1], only those solutions will be entered in the table which meet the required coefficients of safety. Recommended values are provided on the right of the entry field.

Parameters of the tooth profile. [3] Parameters of the tooth profile can be changed within a wide range and are often dependent on the manufacturing possibilities. The following values are commonly used: Addendum - Coefficient of the height of the tooth head ha* = 1.0 Unit head clearance ca* = 0.25 (0.2,0.3) Coefficient of the root radius rf* = 0.38 Note: Values are entered in module units, which is the mx value for ZA worm (axial module) and the mn value for ZN, ZI, ZK and ZH worms (normal module).

Design of a geometry of toothing. [4] This is the central article of the whole calculation and the worm gearing geometry design. It is divided into three, closely interrelated parts. 1. Proposal of a table of proper solutions [4.1-4.7] 2. Direct design of geometry [4.8-4.22] 3. Design (fine tuning) of precise centre-line distance [4.23-4.25] Recommendation: When designing power gearing, it is recommended to use in any case the "Table of proper solutions". In non-power transmissions or where geometry is known, parameters can be entered right in the second section. 4.1 Table of proper solutions The table of proper solutions is set up as follows: Numbers of worm teeth are entered in the calculation gradually (the range is set in [4.3]); worm diameter quotient q is gradually entered for each value (the range is set in [4.4]); and a minimum module value is searched for every such combination (and/or maximum value DP for inches) which meets the safety coefficients required (selected in [4.2]). After finding all proper solutions, the table is sorted by the parameter set in line [4.5] and the first solution in the table [4.7] is put into the calculation. Start table calculation pressing the “Run the table” push-button. The calculation process is shown in the dialog. Warning: The values of transmission ratio [1.6], pressure angle [4.10] and addendum modification coefficient for worm gear [4.21] are also entered in the table of proper solutions. When selected from the table [4.7], these values are set for the saved values. Therefore, when changing the parameters, recalculate the table of proper solutions. 4.2 Check safety In this line, tick the safety type which must be fulfilled to include the solution in the table of solutions. Set the coefficients in lines [2.14-2.17]. It is recommended to have the check of all coefficients activated. 4.3 Range of z1 from - to In this line, enter the range of worm tooth number z1 for which the table should be solved. Usually z1=1~4 (higher number of worm teeth z1 for higher transmission ratio) is used.

The range of permissible values is z1=1~12, the first value being lower than or equal to the second one. 4.4 Range q from - to In this line, enter the range of diameter quotient q for which the table should be solved. Usually q=8-16 (higher value q for smaller module). The range of permissible values is q=6~25, the first value being lower than or equal to the second one. 4.5 Sort results by parameters Choose by which column the table has to be sorted. 4.6 Table of solutions By selecting a solution from the table, the solution parameters are transferred into the calculation. The small push-button "