【机械仿真】直齿圆柱齿轮应力计算【含GUI Matlab源码 2077期】

⛄一、获取代码方式

获取代码方式1： 完整代码已上传我的资源：【机械仿真】基于matlab GUI直齿圆柱齿轮应力计算【含Matlab源码 2077期】 点击上面蓝色字体，直接付费下载，即可。

获取代码方式2： 付费专栏物理应用（Matlab）

备注： 点击上面蓝色字体付费专栏物理应用（Matlab），扫描上面二维码，付费299.9元订阅海神之光博客付费专栏，凭支付凭证，私信博主，可免费获得5份本博客上传CSDN资源代码（有效期为订阅日起，三天内有效）； 点击CSDN资源下载链接：5份本博客上传CSDN资源代码

⛄二、直齿圆柱齿轮离心应力的计算简介

1引言 在齿轮设计计算中,主要采用齿面接触疲劳强度计算,齿根弯曲疲劳强度计算和齿面胶合计算。而齿根弯曲疲劳强度计算主要考虑了工作过程中的外载荷、各种加工误差及变形引起的惯性力对齿轮强度的影响,没有考虑齿轮工作过程中离心力对齿轮强度的影响。离心力引起的应力,对于高速齿轮传动是一个不可忽视的应力。为了保证齿轮传动的安全,设计齿轮传动更精确,本文推导了高速直齿圆柱齿轮离心应力的计算公式:为了计算的方便,给出了计算离心应力的系数A的数值表。同时,分析了齿数Z对系数A的数值的影响,绘制了系数A的数值随着齿数Z的变化曲线。本文提供了离心应力的计算方法,为齿轮传动的强度计算提供了可靠的依据。在齿根弯曲疲劳强度校核计算时,只需将按设计计算的弯曲应力再叠加一个离心应力,就可以保证齿轮传动更安全工作,设计更准确。

2直齿圆柱齿轮离心力的计算 2.1直齿圆柱齿轮离心力的计算公式 设有一标准直齿圆柱齿轮,模数为m,齿数为Z,分度圆压力角、齿顶圆压力角和齿根圆压力角分别为α、αa、αb;分度圆半径、齿顶圆半径、齿根圆半径和基圆半径分别为r、ra、rf、lb;齿轮宽度为B;工作时的转速为n;齿轮材料的密度为ρ。现在分析半径为ri的圆柱面上,齿厚为si,高为dri的一微面积,如图(1)所示。设该微面积为dAi,则: 这一部分微面积引起的离心力为: 图1 离心力计算简图 将(4)式代入(3)式,可得: 将(5)式两边求定积分,可得: 为了计算(7)式中后两项积分,由图(1)的几何关系可知: ![以上推导的(8)式、(9)式即为直齿圆柱齿轮离心力的计算公式。

2.2公式分析及离心力的简化计算 由(8)式可知:离心力与转速n的平方模数m的立方及系数A成正比;当齿根圆的半径小于基圆半径时,齿根圆位于基圆之内,这时,可取齿根圆压力角αf=0°。

由(8)式可知:系数A与齿数Z成三次函数关系系数A与齿数Z的函数图像如图(2)所示。由图(2)可知:随着齿数Z的增大,系数A将近似于线性增大。当齿数Z小于42时,系数A的计算式中会出现复数和cosαf>1的情况,其原因是齿根圆的半径小于基圆半径,齿根圆位于基圆之内。此时可按αf=0°进行计算,所引起的误差很小。图2 A与Z之间的关系曲线 由离心力F的计算式可知:只要系数A的值计算出来了,离心力F的计算就很容易计算了。为子简化离心力F的计算,可以把系数A的值制成表格如表(1),根据齿数Z的值直接查表而得到系数A的值(或查图(2)),于是,根据(8)式就可以计算离心力F。

3直齿圆柱齿轮离心应力的计算 3.1精确计算离心应力 精确计算离心应力就是在确定危险截面的弦齿厚时,考虑齿根截面的过渡圆弧半径对弦齿厚的影响,通过精确计算得到弦齿厚,从而求得离心应力,下面就是精确计算离心应力的方法。

直齿圆柱齿轮离心力F除以轮齿危险截面面积(齿根截面面积)即可得离心应力计算式: ρao为刀具齿顶过渡圆弧半径,G、θ均为辅助值,可按文[4]的有关公式计算。

3.2简化计算离心应力 简化计算离心应力就是在确定危险截面的弦齿厚时,不考虑齿根截面的过渡圆弧半径对弦齿厚的影响,当齿数Z<42时,以基圆弦齿厚作为齿厚;当齿数Z>42时,以根圆弦齿厚作为齿厚(假设渐开线延续至齿根圆)计算离心应力。由此产生的误差很小,而计算简便易行。

⛄三、部分源代码

function varargout = GEARstress(varargin) % GEARSTRESS M-file for GEARstress.fig % GEARSTRESS, by itself, creates a new GEARSTRESS or raises the existing % singleton*. % % H = GEARSTRESS returns the handle to a new GEARSTRESS or the handle to % the existing singleton*. % % GEARSTRESS(‘CALLBACK’,hObject,eventData,handles,…) calls the local % function named CALLBACK in GEARSTRESS.M with the given input arguments. % % GEARSTRESS(‘Property’,‘Value’,…) creates a new GEARSTRESS or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before GEARstress_OpeningFunction gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to GEARstress_OpeningFcn via varargin. % % *See GUI Options on GUIDE’s Tools menu. Choose “GUI allows only one % instance to run (singleton)”. % % See also: GUIDE, GUIDATA, GUIHANDLES

% Copyright 2002-2003 The MathWorks, Inc.

% Edit the above text to modify the response to help GEARstress

% Last Modified by GUIDE v2.5 26-Mar-2022 22:55:08

% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct(‘gui_Name’, mfilename, … ‘gui_Singleton’, gui_Singleton, … ‘gui_OpeningFcn’, @GEARstress_OpeningFcn, … ‘gui_OutputFcn’, @GEARstress_OutputFcn, … ‘gui_LayoutFcn’, [] , … ‘gui_Callback’, []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end

if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT

% — Executes just before GEARstress is made visible. function GEARstress_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to GEARstress (see VARARGIN)

movegui(‘center’) %使界面居中 set(handles.text65,‘string’,‘欢迎使用直齿圆柱齿轮应力计算界面’,‘fontsize’,… 16,‘fontweight’,‘bold’); %采用静态文本的办法，给界面添加一个标题，并设置其字体的大小与粗体字 % Choose default command line output for GEARstress handles.output = hObject;

% Update handles structure guidata(hObject, handles); %数据更新

% UIWAIT makes GEARstress wait for user response (see UIRESUME) % uiwait(handles.figure1);

% — Outputs from this function are returned to the command line. function varargout = GEARstress_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure varargout{1} = handles.output;

function edit1_Callback(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,‘String’) returns contents of edit1 as text % str2double(get(hObject,‘String’)) returns contents of edit1 as a double guidata(hObject, handles);

% — Executes during object creation, after setting all properties. function edit1_CreateFcn(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc set(hObject,‘BackgroundColor’,‘white’); else set(hObject,‘BackgroundColor’,get(0,‘defaultUicontrolBackgroundColor’)); end

function edit2_Callback(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,‘String’) returns contents of edit2 as text % str2double(get(hObject,‘String’)) returns contents of edit2 as a double guidata(hObject, handles);

% — Executes during object creation, after setting all properties. function edit2_CreateFcn(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc set(hObject,‘BackgroundColor’,‘white’); else set(hObject,‘BackgroundColor’,get(0,‘defaultUicontrolBackgroundColor’)); end

function edit3_Callback(hObject, eventdata, handles) % hObject handle to edit3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,‘String’) returns contents of edit3 as text % str2double(get(hObject,‘String’)) returns contents of edit3 as a double guidata(hObject, handles);

% — Executes during object creation, after setting all properties. function edit3_CreateFcn(hObject, eventdata, handles) % hObject handle to edit3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc set(hObject,‘BackgroundColor’,‘white’); else set(hObject,‘BackgroundColor’,get(0,‘defaultUicontrolBackgroundColor’)); end

⛄四、运行结果

⛄五、matlab版本及参考文献

1 matlab版本 2014a

2 参考文献 [1] 门云阁.MATLAB物理计算与可视化[M].清华大学出版社，2013. [2]冯剑军,谭援强,张高峰,韩利芬 ,赵又红.高速直齿圆柱齿轮离心应力的计算[J].现代机械. 2003,(04)

3 备注 简介此部分摘自互联网，仅供参考，若侵权，联系删除

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