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Optimal calculation and experimental study on cutting force of hypoid gear processed by generating method

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Abstract

The cutting area and cutting force are important factors that affect the tool life and the machining performance of the machine tool. According to the characteristics and actual working conditions of hypoid gear processed by generating method, a new method for calculating the tangential milling force of multi-cutter teeth is presented. The changing rule of cutting area of the tooth surface is analyzed, the boundaries of the cutting area, such as the meshing line, the intersection line between the tool tip and the face cone of the wheel blank, the intersection line between the tool tip and the end face of wheel blank, are calculated, and the formula for calculating the cutting area is derived. According to the relationship of the motion and position between the cutting tool and workpiece, the dynamic tangential cutting force is calculated. The calculation of constant cutting force is completed based on the optimization of feed velocity, and an example is introduced to calculate the cutting area and cutting force. The experiment of variable tangential cutting force and constant tangential cutting force is completed, and the accuracy of the dynamic cutting force model is verified.

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Abbreviations

r o :

Cutting tool radius

W 1 :

Tool tip distance

α 1 :

Cutting blade profile angle

u t, φ c :

Cutting tool surface coordinates

φ g1 :

Cradle angle

φ 1 :

Workpiece rotation angle

E 1 :

Vertical offset of workpiece

X B2 :

Sliding base

X G2 :

Machine center to back

γ 1 :

Machine root angle

G a :

Distance from face cone vertex to cross point

θ a :

Face angle

u a, φ a :

Surface coordinate of face cone

G b :

Distance from back cone vertex to cross point

θ b :

Back cone angle

u b, φ b :

Back cone surface coordinate

Db :

Diameter of outer circle of the outer end

t :

Actual cutting time

Δt :

The range of time

n p :

Rotating speed of cutting tool

Z p :

Total number of cutting blades

N :

Number of shares of time divided (the time required for the cutting blade to rotate from point X3 to point X1)

d max :

Maximum cutting depth

h max :

Maximum cutting thickness

s i :

Cutting area of each instant

P b :

Fundamental plane

P c :

Cutting edge plane

P n :

Normal plane

P s :

Shear plane

γ n :

Normal rake angle

ϕ r :

Normal shear angle

τ :

Shearing stress

ξ :

Deformation coefficient

η c :

Chip flow angle

η s :

Shear flow angle

η T :

The angle between the plane Pe and the plane Ps

I :

Tool cutting edge inclination angle

τ :

Shearing stress

b :

Cutting thickness

h :

Cutting depth

β :

Friction angle

V p :

Feeding speed

φ cs :

Cutting tool rotation angle

l pp :

Length of the intersection line between the outer cutting tool tip and the wheel blank

l ec :

Length of the intersection line between the inner cutting tool tip and the face cone

A max :

Maximum cutting area

a :

Fitting coefficient

b :

Fitting coefficient

c :

Fitting coefficient

d :

Fitting coefficient

e :

Fitting coefficient

f :

Fitting coefficient

g :

Fitting coefficient

T :

Motor output torque

F t :

Tangential cutting force produced by cutting tool

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Funding

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 52005157, No. 51705135 and No. 51975185).

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Authors and Affiliations

  1. Henan Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing, Henan University of Science and Technology, Luoyang, 471003, China

    Chuang Jiang, Jing Deng & Xiaozhong Deng

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  1. Chuang Jiang
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  2. Jing Deng
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  3. Xiaozhong Deng
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Correspondence to Chuang Jiang.

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Jiang, C., Deng, J. & Deng, X. Optimal calculation and experimental study on cutting force of hypoid gear processed by generating method. Int J Adv Manuf Technol 113, 1615–1635 (2021). https://doi.org/10.1007/s00170-020-06477-2

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  • DOI: https://doi.org/10.1007/s00170-020-06477-2

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