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Prediction model for surface generation mechanism and roughness in face gear grinding

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Abstract

Owing to the complexity of the movement and contact relationships between grinding wheel and face gear, the previous surface prediction models for cylindrical, flat, and internal grinding are not able to reveal the surface generation mechanism in face gear generating grinding. In this work, according to the contact conditions between face gear and grinding wheel, grinding width and contact arc length were calculated. Based on the mapping relationship between face gear and wheel grain derived from theory of gearing, generation mechanism of face gear was revealed based on material removal of one step, single path, and entire surface of face gear. From this study, it is concluded that (1) swing angle increment of grinding wheel affects the grinding overlapping width and is the most significant factor affecting the tooth surface roughness. (2) The axial profile of grinding wheel geometry is the basic reason of uneven tooth surface topography. After optimizing the swing angle increment in different regions of face gear, an overall uniform morphology can be obtained efficiently. Experimental results show reasonable consistency with numerical simulations that validate the proposed model. This work provided a novel prediction model for surface generation mechanism and roughness for face gear grinding and can be utilized to optimize the process parameters to obtain higher tooth surface integrity.

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Data availability

We confirm that data is open and transparent.

Code availability

The codes generated during the current study are available from the corresponding author on reasonable request.

Abbreviations

a n :

Normal cutting depth of grains

a n,k :

Normal cutting depth of grain k at point d

\({a}_{n,k,{q}_{m}}\) :

The corrected value for an,k

\({a}_{n,k,q}\) :

Normal cutting depth of grain k when j = q

a p :

Cutting depth

b 1, b 2 :

Boundary points of the grinding width of grain k

\({b}_{k,o},{b}_{k,i}\) :

The maximum gap width of grain k when j = qm

d :

One point on contact line

d alo :

Grinding allowance of the face gear

\(\Delta d\) :

Meshing spacing

h c,k :

Protrusion height of the grain at the position of c and k on the wheel surface

h max :

The maximum protrusion height of the grains

h k :

Protrusion height of grain k

h x , k , q :

Protrusion heights of grain k in the xs0 direction when j = q

h z , k , q :

Protrusion heights of grain k in the zs0 direction when j = q

i, j :

Grid indices in the axial and involute profile direction of pinion

i f :

Transmission ratio of face gear pair

\({i}_{k,o},\ {i}_{k,i}\)  :

The index values of i for \({b}_{k,o}\) and \({b}_{k,i}\)

\({j}_{k,o},\ {j}_{k,i}\)  :

The index values of j for \({b}_{k,o}\) and \({b}_{k,i}\)

k :

Curvature of wheel profile

l 1,l 2 :

Overlapping width and non-overlapping width of the n-th grinding path

L :

Arc length between adjacent grains

M :

Grain size number

\({\mathbf{M}}_{2s}\) :

Transformation matrix from \({S}_{s}\) to \({S}_{2}\)

\({\mathbf{M}}_{2p}\) :

Transformation matrix from \({S}_{p}\) to \({S}_{2}\)

\({\mathbf{M}}_{pm}\) :

Transformation matrix from \({S}_{m}\) to \({S}_{p}\)

\({\mathbf{M}}_{ms}\) :

Transformation matrix from \({S}_{s}\) to \({S}_{2}\)

\({\mathbf{M}}_{s0,s}\) :

Transformation matrix for obtaining the involute profile of grinding wheel

\({\mathbf{M}}_{t0,s0}\) :

Transformation matrix for obtaining wheel profile in coordinate system St

\({\mathbf{M}}_{t,t0}\) :

Transformation matrix for obtaining the overall profile of grinding wheel

N g :

Normal vector of the wheel profile at point p

n :

Rotation speed of grinding wheel

\(\left({n}_{gx,q},{n}_{gz,q}\right)\) :

Normal vector coordinates when j = q

\(\left({n}_{gx,k},{n}_{gz,k}\right)\) :

Normal vector coordinates when j = b

P in :

Approach point

P out :

Recess point

P ha :

Addendum interference point

P hf :

Final point of transition curve

p :

The center of the bottom surface of grain k

p k + 1 :

The center of the bottom surface of (k + 1)-th grain

q m :

The corrected value for q

R k :

Rotation radius of grain k

R 2 :

\({\phi }_{\mathrm{sin}}\)’S corresponding radius

S p (x p, y p, z p):

Coordinate rigidly connected to the pinion

S m (x m, y m, z m):

Coordinate rigidly connected to the face gear

S s (x s, y s, z s):

Follow-up coordinate systems of pinion

S 2 (x 2, y 2, z 2):

Follow-up coordinate systems of face gear

S t (x t, y t, z t):

Coordinate system of grinding wheel

\({t}_{qm}\) :

The movement time when j = qm

\({u}_{s}\) :

Tooth width parameter of pinion

\({v}_{s,k}\) :

Cutting speed of grain k

v w :

Feed rate of the face gear

(x k , p, z k , p):

Coordinates of point p / coordinates when j = b

\(\left({x}_{k+1,p1},{z}_{k+1,p1}\right)\) :

Coordinates of point pk+1

\(\left({x}_{q},{z}_{q}\right)\) :

Coordinates when j = q

(x i, z i), (i = 1, 2) :

Coordinates of b1 and b2

z s :

Teeth number of pinion

\({\phi }_{s \mathrm{min}}\) :

Rotation angle of pinion

\(\Delta {\phi }_{s}\) :

Swing angle increments of grinding wheel

\({\phi }_{s\ \mathrm{max}}\)  :

Upper limit of the angle \({\phi }_{s}\)

\({\phi }_{s\ \mathrm{min}}\)  :

Lower limit of the angle \({\phi }_{s}\)

\({\phi }_{2}\) :

Rotation angle of face gear

\({\phi }_{\mathrm{sin}}\) :

Limiting angle of point Pin

\({\phi }_{sha}\) :

Limiting angle of point Pha

\({\phi }_{out}\) :

Limiting angle of point Pout

\({\phi }_{shf}\) :

Limiting angle of point Phf

\({\theta }_{s}\) :

Roll angle of involute

\({\theta }_{sha}\) :

Roll angle corresponding to the dedendum of pinion

\({\theta }_{s\ \mathrm{max}}\)  :

Roll angle corresponding to the addendum of pinion

θ i :

Roll angle of (k + 1)-th grain

\({\theta }_{k,i}\) :

Angle between the normal vectors of the profile point (xi, yi) and (xk,p, zk,p)

\({\theta }_{u},{\theta }_{d}\) :

Roll angles corresponding to b1 and b2

μ :

Mean value of grain diameter distribution

σ :

Standard deviation of grain diameter distribution

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Funding

This work was funded by the National Natural Science Foundation of China (No: 51905459), State Key Laboratory of Mechanical Transmission, Chongqing University (No. SKLMT-MSKFKT-202003), and Aero Engine Corporation of China’s 2019 Industry-University-Research Cooperation Project (No: HFZL2019CXY025).

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Authors and Affiliations

  1. School of Aerospace Engineering, Xiamen University, Xiamen, 361005, China

    Xiaofan Ma, Zhiqin Cai, Bin Yao, Sijie Cai & Wanshan Liu

  2. Department of Mechanical and Electrical Engineering, Xiamen University Tan Kah Kee College, Zhangzhou, 363105, China

    Guanfeng Chen

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  1. Xiaofan Ma
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  2. Zhiqin Cai
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  3. Bin Yao
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Contributions

Xiaofan Ma: Methodology, data curation, formal analysis, validation, and writing–original draft and editing. Zhiqin Cai: Funding acquisition, writing (review), and revision. Bin Yao: Funding acquisition, resource supervision, and project administration. Guanfeng Chen: Conceptualization. Sijie Cai: Resources. Wanshan Liu: Investigation and software.

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Correspondence to Zhiqin Cai.

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Ma, X., Cai, Z., Yao, B. et al. Prediction model for surface generation mechanism and roughness in face gear grinding. Int J Adv Manuf Technol 120, 4423–4442 (2022). https://doi.org/10.1007/s00170-022-09035-0

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