DESIGN KALKULASI RODA GIGI LURUS (SPUR GEAR)

 

 

 Spur Gears are the simplest type of gear. The calculations for spur gears are also simple and they are used as the basisfor the calculations for other types of gears. This section introduces calculation methods of standard spur gears, profileshifted spur gears, and linear racks. The standard spur gear is a non-profile-shifted spur gear.
(1) Standard Spur Gear
Figure 4.1 shows the meshing of standard spur gears. The meshing of standard spur gears means the reference circlesof two gears contact and roll with each other. The calculation formulas are in Table 4.1.

Fig. 4.1 The Meshing of Standard Spur Gears
( α=20°, z1=12, z2=24, x1=x2=0 )
Table 4.1 Calculations for Standard Spur Gears

No.	Item	Symbol	Formula	Example
				Pinion (1)	Gear (2)
1	Module	m	Set Value	3
2	Reference Pressure Angle	α		20 deg
3	Number of Teeth	z		12	24
4	Center Distance	a	NOTE1	54.000
5	Reference Diameter	d	zm	36.000	72.000
6	Base Diameter	db	d cos α	33.829	67.658
7	Addendum	ha	1.00m	3.000	3.000
8	Tooth Depth	h	2.25m	6.750	6.750
9	Tip Diameter	da	d + 2m	42.000	78.000
10	Root Diameter	df	d – 2.5m	28.500	64.500

NOTE 1 : The subscripts 1 and 2 of z1 and z2 denote pinion and gear
All calculated values in Table 4.1 are based upon given module m and number of teeth (z1 and z2). If instead, the modulem, center distance a and speed ratio i are given, then the number of teeth, z1 and z2, would be calculated using theformulas as shown in Table 4.2.
Table 4.2 The Calculations for Number of Teeth

No.	Item	Symbol	Formula		Example
					Pinion (1)	Gear (2)
1	Module	m	Set Value		3
2	Center Distance	a			54.000
3	Speed Ratio	i			1.25
4	Sum of No. of Teeth	z1 + z2			36
5	Number of Teeth	z			16	20

Note, that the number of teeth will probably not be integer values when using the formulas in Table 4.2. In this case,it will be necessary to resort to profile shifting or to employ helical gears to obtain as near a transmission ratioas possible.
(2) Profile Shifted Spur Gear
Figure 4.2 shows the meshing of a pair of profile shifted gears. The key items in profile shifted gears are the operating(working) pitch diameters (dw) and the working (operating) pressure angle (αw). These values are obtainable from themodified center distance and the following formulas :


Fig. 4.2 The Meshing of Profile Shifted Gears
( α=20°, z1=12, z2=24, x1=+0.6, x2=+0.36 )
In the meshing of profile shifted gears, it is the operating pitch circle that is in contact and roll on each other thatportrays gear action. Table 4.3 presents the calculations where the profile shift coefficient has been set at x1 andx2 at the beginning. This calculation is based on the idea that the amount of the tip and root clearance should be 0.25m.
Table 4.3 The Calculations for Profile Shifted Spur Gears (1)

No.	Item	Symbol	Formula	Example
				Pinion (1)	Gear (2)
1	Module	m	Set Value	3
2	Reference Pressure Angle	α		20 deg
3	Number of Teeth	z		12	24
4	Profile Shift Coefficient	X		0.6	0.36
5	Involute αw	inv αw		0.034316
6	Working Pressure Angle	αw	Find from Involute Function Table	26.0886 deg
7	Center Distance Modification Coefficient	y		0.83329
8	Center Distance	a		56.4999
9	Reference Diameter	d	zm	36.000	72.000
10	Base Diameter	db	d cos α	33.8289	67.6579
11	Working Pitch Diameter	dw		37.667	75.333
12	Addendum	ha1 ha2	( 1 + y – x2 ) m ( 1 + y – x1 ) m	4.420	3.700
13	Tooth Depth	h	{2.25 + y – ( x1 + x2 )}m	6.370
14	Tip Diameter	da	d + 2ha	44.840	79.400
15	Root Diameter	df	da – 2h	32.100	66.660

A standard spur gear is, according to Table 4.3, a profile shifted gear with 0 coefficient of shift; that is , x1=x2=0.
Table 4.4 is the inverse formula of items from 4 to 8 of Table 4.3.
Table 4.4 The Calculations for Profile Shifted Spur Gears (2)

No.	Item	Symbol	Formula	Example
				Pinion (1)	Gear (2)
1	Center Distance	a	Set Value	56.4999
2	Center Distance Modification Coefficient	y		0.8333
3	Working Pressure Angle	αw		26.0886 deg
4	Sum of Profile Shift Coefficient	x1 + x2		0.9600
5	Profile Shift Coefficient	x	–	0.6000	0.3600

There are several theories concerning how to distribute the sum of profile shift coefficient (x1 + x2) into pinion (x1)and gear (x2) separately. BSS (British) and DIN (German) standards are the most often used. In the example above, the12 tooth pinion was given sufficient correction to preventundercut, and the residual profile shift was given to the mating gear.
(3) Rack and Spur Gear
Table 4.5 presents the method for calculating the mesh of a rack and spur gear.
Figure 4.3 (1) shows the the meshing of standard gear and a rack. In this mesh, the reference circle of the gear touchesthe pitch line of the rack.
Figure 4.3 (2) shows a profile shifted spur gear, with positive correction xm, meshed with a rack. The spur gear hasa larger pitch radius than standard, by the amount xm. Also, the pitch line of the rack has shifted outward by the amountxm.
Table 4.5 presents the calculation of a meshed profile shifted spur gear and rack. If the profile shift coefficientx1 is 0, then it is the case of a standard gear meshed with the rack.
Table 4.5 The calculations of dimensions of a profile shifted spur gear and a rack

No.	Item	Symbol	Formula	Example
				Spur gear	Rack
1	Module	m	Set Value	3
2	Reference pressure angle	a		20 deg
3	Number of teeth	z		12	–
4	Profile shift coefficient	x		0.6
5	Height of pitch line	H		–	32.000
6	Working pressure angle	αw		20 deg
7	Mounting distance	a		51.800
8	Reference diameter	d	zm	36.000	–
9	Base diameter	db	d cos α	33.829
10	Working pitch diameter	dw		36.000
11	Addendum	ha	m ( 1 + x )	4.800	3.000
12	Tooth depth	h	2.25m	6.750
13	Tip diameter	da	d + 2ha	45.600	–
14	Root diameter	df	da – 2h	32.100

One rotation of the spur gear will displace the rack l one circumferential length of the gear’s reference circle,per the formula :

The rack displacement, l, is not changed in any way by the profile shifting. Equation (4.2) remains applicable for anyamount of profile shift.

Fig. 4.3 (1) The meshing of standard spur gear and rack
( α=20°, z1=12, x1=0 )

Fig. 4.3 (2) The meshing of profile shifted spur gear and rack
( α=20°, z1=12, x1=+ 0.6 )

 

Rumus yang dipakai : 

No       Simbol        Keterangan                Rumus 

1.             M               Modul                     M = Dp/Z 

                                                                  M = Dk/(Z+2) 

2              Z             Jumlah gigi                Z  = Dp/M 

3             Dk         Diameter kepala           Dk = (Z+2).M 

4             Dp         Diameter pitch             Dp = Z.M 

5             Df          Diameter kaki              Df = Dp+(2.M) 

                                                                  Df = (Z-2,5)M 

6             Hk         Tinggi kepala kaki      1.M 

7             Hf          Tinggi kaki gigi          1,16.M 

8             H           Tinggi kaki                  2,16.M 

9             B            Lebar gigi                   10.M