Hydraulic Power Steering Gear Design

Selection of material

Factorability and reliability were also considered.
Based on this Aluminum T6 7075 were selected.

Module m = 3 mm (assume)

Gear ratio G = 16 (assume)
Pressure angle φ = 20°
Helical angle is from 20° to 45° (take α = 30°)
Number of pinion and gear teeth Z_P=7 teeth (assume)

Required

Dimensions of pinion and gear
Check the wear, bending, dynamic and other strength of gear

S. No.	Parameters or Dimensions	General formula	Pinion dimensions [mm]	Gear dimensions [mm]
1	Module (m)		3	3
2	Transverse pitch (Pt)	Pt = π*m	9.42	9.42
3	Number of teeth (Z)		112	112
4	Pitch circle diameter Do	Do = m*Z	21
5	Addendum	0.8*m	2.4	2.4
6	Deddendum	1*m	3	3
7	Root circle diameter Dr	Do-2* deddendum	15
8	Crown circle diameter Dk	Do + 2* addendum	27
9	Depth of the tooth (h)	Addendum + dedendum	5.4	5.4
10	Depth of working tooth (hw)	1.6*m	4.5	4.8
11	Tooth thickness (t)	1.5708*m	4.7124	4.7124
12	Fillet radius at root	0.4*m	1.2	1.2
13	Minimum clearance (c)	deddendum-addendum	0.6	0.6
14	Face width b	b = 1.15*Pt/tan α	18.7633	17.7633

Gear Parameter Analysis

• The normal and axial pitch of the pinion and gear can be determined from the geometric analysis of the figure below.

p_n = p_tcosα = 9.42 cos30° = 8.158mm

p_x= pt/tan α = 9.42 mm/tan30° = 16.316mm

The transverse pressure angle φ_t = tan^-1 (tan φn/cosα) = tan^-1 (tan 20°/cos30°) = 22.8°

(same for all gears and pinions)

Force analysis

Beam Strength of Gear Teeth – Lewis Equation

The maximum value of the bending stress (or the permissible working stress), at the section BC is given by

Iσ_w = M.Y       Y=t/2

Where, M = Maximum bending moment at the critical section BC =WT×h,

I = Moment of inertia about the center line of the tooth = b.t³/12,

By substituting these values into the above equation we get;

Lewis equation is applied only to the weaker of the two wheels. When both the pinion and the gear are made of the same material, then pinion is the weaker.

Permissible working (bending) Stress for Gear Teeth in the Lewis Equation

According to the Barth formula, the permissible working stress,

Where σo= Allowable static stress, and

Cv= Velocity factor

 for the peripheral velocities 5m/s to 10 m/s.

σ_p =180.33

σ_w = 180.33× 0.545=98.36 MPa

600 = σ_w × 19 × π*3*0.175

σ_w= 19 Mpa The factor of safety F.s = 98.36 Mpa / 19Mpa = 5.3, therefore the calculated face width b is satisfactory.