程 準(zhǔn)，魯植雄

拖拉機(jī)液壓傳動(dòng)系統(tǒng)特性模型修正與參數(shù)辨識(shí)

程 準(zhǔn)1，魯植雄2

（1. 南京林業(yè)大學(xué)汽車與交通工程學(xué)院，南京 210037；2. 南京農(nóng)業(yè)大學(xué)工學(xué)院，南京 210031）

精準(zhǔn)描述無級(jí)變速系統(tǒng)特性是拖拉機(jī)動(dòng)力裝置設(shè)計(jì)和控制策略制定的前提，是節(jié)能減排和動(dòng)力提高的關(guān)鍵。為解決拖拉機(jī)常用無級(jí)變速系統(tǒng)特性隨工況變化而導(dǎo)致原理論模型精度受限問題，該研究對(duì)受工況影響最為顯著的液壓傳動(dòng)系統(tǒng)的調(diào)速和效率特性進(jìn)行研究。采用臺(tái)架試驗(yàn)獲取液壓傳動(dòng)系統(tǒng)特性的樣本數(shù)據(jù)，基于偏最小二乘法對(duì)比不同工況對(duì)調(diào)速和效率特性的影響，結(jié)合原理論模型和改進(jìn)的模擬退火算法，提出液壓傳動(dòng)系統(tǒng)特性的模型修正及其參數(shù)辨識(shí)方法，并分別建立調(diào)速特性和效率特性的改進(jìn)半經(jīng)驗(yàn)?zāi)Ｐ?。結(jié)果表明，輸入轉(zhuǎn)速和輸出端負(fù)載轉(zhuǎn)矩對(duì)調(diào)速特性的影響程度分別為0.36和0.92；輸入轉(zhuǎn)速、輸出端負(fù)載轉(zhuǎn)矩和排量比對(duì)效率特性的影響程度分別為0.05、0.71和0.26；修正后模型參數(shù)較少，辨識(shí)容易，且精度高，估測(cè)值與實(shí)際值基本吻合（2參數(shù)調(diào)速特性半經(jīng)驗(yàn)?zāi)Ｐ偷臎Q定系數(shù)2為0.97、平均絕對(duì)百分比誤差為7.93%，5參數(shù)效率特性半經(jīng)驗(yàn)?zāi)Ｐ偷臎Q定系數(shù)2為0.93、平均絕對(duì)百分比誤差為2.50%）。研究以期為拖拉機(jī)等農(nóng)業(yè)機(jī)械的動(dòng)力傳動(dòng)裝置的特性分析與評(píng)估、優(yōu)化設(shè)計(jì)和控制策略制定提供依據(jù)和參考。

拖拉機(jī)；無級(jí)變速；調(diào)速特性；效率特性；參數(shù)辨識(shí)；半經(jīng)驗(yàn)?zāi)Ｐ?/p>

0 引 言

拖拉機(jī)是最為重要的農(nóng)業(yè)作業(yè)機(jī)械之一[1-3]，其作業(yè)工況惡劣復(fù)雜，這對(duì)拖拉機(jī)動(dòng)力傳動(dòng)系統(tǒng)提出了較高要求。液壓機(jī)械無級(jí)變速器（Hydro-Mechanical Continuously Variable Transmission，HMCVT）[4-6]和靜液壓傳動(dòng)（Hydrostatic Transmission，HST）系統(tǒng)[7-9]是應(yīng)用廣泛的先進(jìn)拖拉機(jī)無級(jí)變速系統(tǒng)。

調(diào)速特性和效率特性是無級(jí)變速傳動(dòng)系統(tǒng)的核心性能，對(duì)變速器的設(shè)計(jì)、性能評(píng)估以及控制策略制定等有著極為關(guān)鍵的作用。Macor等[10-11]研究指出HMCVT的優(yōu)化設(shè)計(jì)復(fù)雜且具有較強(qiáng)的非線性特點(diǎn)，并采用粒子群算法進(jìn)行多目標(biāo)優(yōu)化設(shè)計(jì)。Zhang等[12]采用非支配排序遺傳算法對(duì)行星排結(jié)構(gòu)參數(shù)以及變速器傳動(dòng)比進(jìn)行優(yōu)化。Sung等[13]采用網(wǎng)絡(luò)分析方法研究了12種HMCVT的調(diào)速特性。于今等[14]提出一種HMCVT系統(tǒng)，建立了調(diào)速特性和功率分流特性理論模型，并采用樣機(jī)試驗(yàn)基于一定工況分析了系統(tǒng)調(diào)速特性以及效率特性等。李娟玲等[15]在Matlab環(huán)境下對(duì)研究所建立的調(diào)速特性和效率特性模型進(jìn)行拖拉機(jī)HMCVT動(dòng)態(tài)特性仿真分析與性能評(píng)估。Xia等[16]基于無級(jí)變速器工作原理推導(dǎo)得出了轉(zhuǎn)速、轉(zhuǎn)矩、效率等特性的變化關(guān)系式，并基于此分析了HMCVT的工作優(yōu)點(diǎn)。Li等[17]采用改進(jìn)的快速非支配排序遺傳算法對(duì)拖拉機(jī)HMCVT進(jìn)行多目標(biāo)優(yōu)化，該方法具有相對(duì)更快的收斂速度。Dai等[18]研制了HMCVT多功能試驗(yàn)臺(tái)，并對(duì)仿真模型進(jìn)行了修正。王光明等[19]采用臺(tái)架試驗(yàn)校準(zhǔn)了基于Simulation X軟件搭建的HMCVT仿真平臺(tái)，并進(jìn)行了特性分析與評(píng)估。孫景彬等[20]設(shè)計(jì)了一種遙控全向調(diào)平山地履帶拖拉機(jī)，整車傳動(dòng)系統(tǒng)采用靜液壓驅(qū)動(dòng)技術(shù)設(shè)計(jì)。此外，張明柱等[21-24]基于對(duì)HMCVT調(diào)速特性和效率特性的分析進(jìn)而研究提升整車使用性能的控制策略。文獻(xiàn)[25]采用偏最小二乘法探究了不同類型因素對(duì)拖拉機(jī)無級(jí)變速系統(tǒng)動(dòng)載荷特性的影響程度。文獻(xiàn)[26-27]采用改進(jìn)的模擬退火算法分別進(jìn)行了拖拉機(jī)驅(qū)動(dòng)系統(tǒng)效率特性模型建立和車輛傳動(dòng)系統(tǒng)優(yōu)化設(shè)計(jì)研究。

綜上，目前對(duì)于無級(jí)變速系統(tǒng)（HST和HMCVT）已有一定的研究，且多集中于特性分析與評(píng)估、優(yōu)化設(shè)計(jì)和控制策略制定。精準(zhǔn)描述和解釋無級(jí)變速系統(tǒng)調(diào)速特性和效率特性是上述研究的必要前提。拖拉機(jī)無級(jí)變速系統(tǒng)由機(jī)械系統(tǒng)（主要包括定軸齒輪副和行星輪系）和液壓系統(tǒng)（主要為泵和馬達(dá)）組成。在傳動(dòng)過程中，機(jī)械系統(tǒng)實(shí)際傳動(dòng)特性與理論傳動(dòng)特性基本吻合，但液壓系統(tǒng)受使用工況影響程度較大，這導(dǎo)致液壓系統(tǒng)實(shí)際傳動(dòng)特性與理論傳動(dòng)特性存在一定程度偏差。而在研發(fā)設(shè)計(jì)階段改進(jìn)拖拉機(jī)無級(jí)變速系統(tǒng)特性模型精度較困難，只能在樣機(jī)制造后進(jìn)行特性對(duì)比驗(yàn)證，這會(huì)造成研發(fā)成本以及研發(fā)周期的增加。目前已有研究采用固定常數(shù)值或純理論表達(dá)式解釋系統(tǒng)特性，也有部分研究通過校準(zhǔn)后的仿真模型進(jìn)行特性數(shù)據(jù)獲取，但這些方法忽略了使用工況的影響，實(shí)測(cè)樣本數(shù)量有限，模型修正方法的應(yīng)用效果有待改進(jìn)，模型參數(shù)辨識(shí)的有效性相對(duì)較低等。

本文基于拖拉機(jī)液壓傳動(dòng)系統(tǒng)試驗(yàn)臺(tái)架，對(duì)其調(diào)速特性和效率特性分別開展多工況測(cè)試，采用偏最小二乘法分析特性影響因素，提出基于改進(jìn)的模擬退火算法和理論模型的半經(jīng)驗(yàn)?zāi)Ｐ托拚c參數(shù)辨識(shí)方法，對(duì)比驗(yàn)證了修正后特性模型的精度，以期為拖拉機(jī)等農(nóng)業(yè)機(jī)械及其他機(jī)械裝置中無級(jí)變速系統(tǒng)特性分析與評(píng)估、優(yōu)化設(shè)計(jì)和控制策略制定提供直接性依據(jù)。

1 液壓傳動(dòng)系統(tǒng)工作原理及試驗(yàn)臺(tái)架

1.1 液壓傳動(dòng)系統(tǒng)工作原理

液壓傳動(dòng)系統(tǒng)總成主要包括泵、馬達(dá)、泵前齒輪、馬達(dá)后齒輪、離合器以及傳動(dòng)軸。為匹配拖拉機(jī)HST和HMCVT的工作要求，本研究采用的傳動(dòng)方案為：動(dòng)力經(jīng)柴油發(fā)動(dòng)機(jī)輸出，通過泵前齒輪系統(tǒng)（傳動(dòng)比分別為1和2）傳遞至“泵-馬達(dá)”系統(tǒng)，再通過馬達(dá)后齒輪系統(tǒng)（傳動(dòng)比3）輸出（此時(shí)濕式離合器C0接合），見圖1。

注：i1～i3為傳動(dòng)比。

本文研究的變量泵-定量馬達(dá)系統(tǒng)采用容積調(diào)速回路，液壓傳動(dòng)系統(tǒng)轉(zhuǎn)速和轉(zhuǎn)矩的關(guān)系式為：

式中n為發(fā)動(dòng)機(jī)轉(zhuǎn)速，r/min；為變量泵的排量比；0為其他傳動(dòng)系總傳動(dòng)比；n為液壓傳動(dòng)系統(tǒng)輸出轉(zhuǎn)速，r/min；T、T、T分別為馬達(dá)輸出轉(zhuǎn)矩、液壓傳動(dòng)系統(tǒng)輸出轉(zhuǎn)矩和拖拉機(jī)傳動(dòng)系末端負(fù)載轉(zhuǎn)矩，N·m。

1.2 試驗(yàn)臺(tái)架

本文研究所用的拖拉機(jī)泵-馬達(dá)系統(tǒng)為HPV-02型變量泵和HMF-02型定量馬達(dá)，排量皆為55 cm3/r，持續(xù)工作功率分別為75和93 kW，額定工作壓力為42 MPa，試驗(yàn)臺(tái)架具體如圖2所示。

①發(fā)動(dòng)機(jī)（道依茨TCD2013L062V）②液壓傳動(dòng)系統(tǒng)③ZJ-5000A型轉(zhuǎn)速轉(zhuǎn)矩傳感器④副齒輪箱⑤DW250型電渦流測(cè)功機(jī)⑥液壓系統(tǒng)（實(shí)現(xiàn)潤(rùn)滑、冷卻等功能）

發(fā)動(dòng)機(jī)和液壓傳動(dòng)系統(tǒng)的輸出端分別連接ZJ-2000A型和ZJ-5000A型轉(zhuǎn)速轉(zhuǎn)矩傳感器（中國江蘇蘭菱），其轉(zhuǎn)速量程分別為0～3 000和0～5 000 r/min，轉(zhuǎn)矩量程分別為0～2 000和0～4 000 N·m。對(duì)試驗(yàn)臺(tái)架進(jìn)行基本的性能測(cè)試試驗(yàn)：固定發(fā)動(dòng)機(jī)轉(zhuǎn)速，調(diào)節(jié)變量泵的排量比分別為0.200、0.250、0.300、0.375、0.500、0.625、0.750和1.000，測(cè)量發(fā)動(dòng)機(jī)轉(zhuǎn)速和轉(zhuǎn)矩、液壓傳動(dòng)系統(tǒng)轉(zhuǎn)速和排量比；固定發(fā)動(dòng)機(jī)轉(zhuǎn)速、排量比和輸出端負(fù)載，濕式離合器連續(xù)接合和斷開3次，測(cè)量發(fā)動(dòng)機(jī)轉(zhuǎn)速和輸出端負(fù)載。

根據(jù)試驗(yàn)結(jié)果（見圖3），扭矩波動(dòng)范圍約±2 N·m，轉(zhuǎn)速波動(dòng)范圍約±3 r/min，輸出轉(zhuǎn)速與排量比正相關(guān)且排量比固定時(shí)輸出轉(zhuǎn)速平穩(wěn)，試驗(yàn)臺(tái)架的基本性能良好。

圖3 試驗(yàn)臺(tái)架的基礎(chǔ)性能測(cè)試結(jié)果

2 調(diào)速特性及其影響因素分析

2.1 調(diào)速特性理論計(jì)算模型

采用傳動(dòng)比變化特性表征調(diào)速特性。結(jié)合式（1），液壓傳動(dòng)系統(tǒng)的傳動(dòng)比（即調(diào)速特性理論計(jì)算模型）為

2.2 調(diào)速特性全因子試驗(yàn)

圖4 調(diào)速特性全因子試驗(yàn)結(jié)果（排量比為1）

偏最小二乘法（Partial Least Squares，PLS）綜合了多元線性回歸、典型相關(guān)分析和主成分分析，能夠較好地解釋每一個(gè)自變量對(duì)因變量的影響程度。本文采用PLS以發(fā)動(dòng)機(jī)轉(zhuǎn)速和輸出端負(fù)載轉(zhuǎn)矩為自變量對(duì)圖4結(jié)果進(jìn)行分析，得到發(fā)動(dòng)機(jī)轉(zhuǎn)速和輸出端負(fù)載轉(zhuǎn)矩對(duì)調(diào)速特性的影響程度（取絕對(duì)值）分別為0.36和0.92。輸出端負(fù)載轉(zhuǎn)矩對(duì)調(diào)速特性影響較大，而發(fā)動(dòng)機(jī)轉(zhuǎn)速所引起的調(diào)速特性平均波動(dòng)僅為1.65%，發(fā)動(dòng)機(jī)轉(zhuǎn)速對(duì)調(diào)速特性影響較小，因此本文調(diào)速特性研究忽略發(fā)動(dòng)機(jī)轉(zhuǎn)速影響。

2.3 輸出端負(fù)載轉(zhuǎn)矩和排量比的全因子試驗(yàn)

由于柱塞式變量泵正偏和反偏時(shí)僅為系統(tǒng)旋轉(zhuǎn)方向不同，因此本文研究忽略變量泵正偏和反偏的影響，即不考慮排量比的正負(fù)性。試驗(yàn)以輸出端負(fù)載轉(zhuǎn)矩（11水平，同2.2節(jié)）和排量比為因素，固定發(fā)動(dòng)機(jī)轉(zhuǎn)速1 280 r/min。排量比變化范圍為0～1，排量比為0時(shí)，定量馬達(dá)不工作，因此除去該情況，以0.250為步長(zhǎng)，考察0.500～0.750之間的調(diào)速特性規(guī)律，補(bǔ)充中間值0.625，共形成5個(gè)水平，分別為1.000、0.750、0.625、0.500和0.250。全因子試驗(yàn)共獲得55組樣本數(shù)據(jù)，統(tǒng)計(jì)結(jié)果見圖5。

圖5 考慮負(fù)載轉(zhuǎn)矩和排量比的調(diào)速特性全因子試驗(yàn)結(jié)果

觀察圖5可知，調(diào)速特性關(guān)于排量比和輸出端轉(zhuǎn)矩分別呈非線性和線性變化；相較于排量比，輸出端轉(zhuǎn)矩的影響程度較??；當(dāng)排量比減小時(shí)，輸出端轉(zhuǎn)矩的影響程度也伴隨性增加。

3 效率特性及其影響因素分析

3.1 效率特性理論計(jì)算模型

常用的變量泵和定量馬達(dá)效率特性理論計(jì)算模型為

式中、、分別為變量泵效率、容積效率和機(jī)械效率；、、分別為變量泵層流泄漏系數(shù)、層流阻力系數(shù)和機(jī)械阻力系數(shù)；Δ為系統(tǒng)壓力差；為液壓油動(dòng)力黏度；、分別為變量泵轉(zhuǎn)速和定量馬達(dá)轉(zhuǎn)速；、、分別為定量馬達(dá)效率、容積效率和機(jī)械效率；、、分別為定量馬達(dá)層流泄漏系數(shù)、層流阻力系數(shù)和機(jī)械阻力系數(shù)。

結(jié)合式（4）與式（5），效率特性主要與排量比、系統(tǒng)壓力差和輸入轉(zhuǎn)速有關(guān)。系統(tǒng)壓力差與負(fù)載轉(zhuǎn)矩正相關(guān)，所以效率特性與排量比、負(fù)載轉(zhuǎn)矩和輸入轉(zhuǎn)速有關(guān)。

3.2 效率特性全因子試驗(yàn)

基于試驗(yàn)臺(tái)架進(jìn)行液壓傳動(dòng)系統(tǒng)效率特性工況因素的全因子試驗(yàn)。試驗(yàn)因素取發(fā)動(dòng)機(jī)轉(zhuǎn)速（3個(gè)水平，同2.2節(jié)）、輸出端負(fù)載轉(zhuǎn)矩（11個(gè)水平，同2.2節(jié)）和排量比（5個(gè)水平，同2.3節(jié)），共獲得165組樣本數(shù)據(jù)，統(tǒng)計(jì)結(jié)果見圖6。

圖6 不同排量比下效率特性全因子試驗(yàn)結(jié)果

采用PLS以發(fā)動(dòng)機(jī)轉(zhuǎn)速、輸出端負(fù)載轉(zhuǎn)矩和排量比為自變量對(duì)圖6結(jié)果進(jìn)行分析，得到發(fā)動(dòng)機(jī)轉(zhuǎn)速、輸出端負(fù)載轉(zhuǎn)矩和排量比對(duì)效率特性的影響程度（取絕對(duì)值）分別為0.05、0.71和0.26。輸出端負(fù)載轉(zhuǎn)矩對(duì)效率特性影響程度大，其次為排量比，而發(fā)動(dòng)機(jī)轉(zhuǎn)速影響較小。因此，本文效率特性研究忽略發(fā)動(dòng)機(jī)轉(zhuǎn)速影響。

4 調(diào)速特性和效率特性模型修正與參數(shù)辨識(shí)

4.1 調(diào)速特性模型修正與參數(shù)辨識(shí)方法

結(jié)合調(diào)速特性實(shí)測(cè)數(shù)據(jù)（圖4和圖5）可知，同一排量比下液壓傳動(dòng)系統(tǒng)傳動(dòng)比與輸出端負(fù)載轉(zhuǎn)矩呈線性正相關(guān)，因此，可設(shè)調(diào)速特性修正模型為

模擬退火算法應(yīng)用Metropolis準(zhǔn)則通過概率性方式獲取最優(yōu)解，在決策變量較少的系統(tǒng)中應(yīng)用效果較好[28]。參考文獻(xiàn)[29]，考慮模擬退火算法的迭代過程主要依托于概率判定，且個(gè)體粒子的產(chǎn)生和擾動(dòng)皆為隨機(jī)過程，本文對(duì)模擬退火算法建立外層循環(huán)，通過多次內(nèi)層循環(huán)迭代獲取最終解。為進(jìn)一步提高算法效率，減少計(jì)算次數(shù)，引入擾動(dòng)次數(shù)自適應(yīng)變化函數(shù)，見式（7）。

式中L為第次擾動(dòng)函數(shù)周期性變更值；1為同一周期內(nèi)層算法執(zhí)行總次數(shù)；為周期數(shù)；M為同一周期第次內(nèi)層算法執(zhí)行后模型估測(cè)值和實(shí)測(cè)值的平均絕對(duì)百分比誤差；3為固定常數(shù)。

4.2 調(diào)速特性模型修正與參數(shù)辨識(shí)結(jié)果

外層循環(huán)200次的I-SA計(jì)算結(jié)果見圖7a，由圖7a可知第159次外層循環(huán)計(jì)算結(jié)果為最優(yōu)解。內(nèi)層循環(huán)的迭代過程見圖7b，根據(jù)最優(yōu)解建立的液壓傳動(dòng)系統(tǒng)調(diào)速特性模型計(jì)算結(jié)果見圖7c。

由圖7a可知，外層循環(huán)初期擾動(dòng)次數(shù)相對(duì)較少，I-SA算法的解波動(dòng)較大，隨后（擾動(dòng)次數(shù)遞增）進(jìn)入平穩(wěn)狀態(tài)，外層循環(huán)第159次結(jié)果最優(yōu)。由圖7b可知，該最優(yōu)結(jié)果與實(shí)測(cè)值的平均絕對(duì)百分比誤差約7.93%。由圖7c可知，修正后模型與實(shí)際測(cè)量結(jié)果吻合度高，決定系數(shù)2約0.97，原理論模型與實(shí)際測(cè)量值之間的平均絕對(duì)百分比誤差約12.09%，修正后模型精度提升34.41%。

4.3 原理論效率特性模型參數(shù)辨識(shí)

外層循環(huán)200次的I-SA算法結(jié)果見圖8a，由圖8a可知，第176次外層循環(huán)計(jì)算結(jié)果最優(yōu)，內(nèi)層循環(huán)的迭代過程見圖8b；根據(jù)最優(yōu)解建立的液壓傳動(dòng)系統(tǒng)效率特性模型計(jì)算結(jié)果見圖8c。

圖7 基于I-SA算法的調(diào)速特性修正模型參數(shù)辨識(shí)結(jié)果

圖8 原理論效率特性模型參數(shù)辨識(shí)結(jié)果

由圖8a可知，外層循環(huán)初期擾動(dòng)次數(shù)相對(duì)較少，I-SA算法的解波動(dòng)較大，隨后（擾動(dòng)次數(shù)遞增）進(jìn)入平穩(wěn)狀態(tài)。外層循環(huán)第176次結(jié)果最為優(yōu)。由圖8b可知，內(nèi)層循環(huán)初期的解波動(dòng)明顯且數(shù)值較大，該最優(yōu)結(jié)果與實(shí)測(cè)值的平均絕對(duì)百分比誤差約4.76%。由圖8c可知，辨識(shí)后原理論效率特性模型與實(shí)際測(cè)量結(jié)果吻合度一般，決定系數(shù)2約0.70，最大誤差約30.25%，辨識(shí)后原理論效率特性模型與實(shí)測(cè)結(jié)果有一定程度的誤差。

4.4 效率特性模型修正與對(duì)比

由于馬達(dá)為定量馬達(dá)，轉(zhuǎn)速影響可忽略，則式（5）輸出值基本僅由負(fù)載轉(zhuǎn)矩決定，且參數(shù)確定時(shí)模型單調(diào)性亦固定，因此定量馬達(dá)理論模型對(duì)效率特性變化的解釋有一定的局限性。變量泵理論模型（待辨識(shí)參數(shù)已合并）關(guān)于負(fù)載轉(zhuǎn)矩和排量比的偏微分分別為

顯然式（8）和式（9）分母皆大于0，且隨排量比和負(fù)載轉(zhuǎn)矩增加而單調(diào)遞增。因此變量泵理論模型的變化特性基本由分子的變化規(guī)律所決定。結(jié)合試驗(yàn)樣本數(shù)據(jù)以及PLS分析結(jié)果，負(fù)載轉(zhuǎn)矩和排量比皆與效率特性正相關(guān)，且隨負(fù)載轉(zhuǎn)矩和排量比的增大效率特性的變化率趨于平穩(wěn)。式（8）和式（9）分子的最高階項(xiàng)分別為關(guān)于負(fù)載轉(zhuǎn)矩的2階項(xiàng)和3階項(xiàng)，因此分子的變化規(guī)律皆可設(shè)計(jì)為大于0且單調(diào)遞減（對(duì)應(yīng)于效率特性遞增且變化率趨于平穩(wěn)情況）。

綜上分析，在參數(shù)選擇合理的情況下，單獨(dú)的3參數(shù)變量泵理論模型可用來描述和解釋效率特性變化。采用4.1節(jié)的外層循環(huán)-I-SA算法對(duì)效率特性模型進(jìn)行參數(shù)辨識(shí)，結(jié)果如下：外層循環(huán)第154次獲得最優(yōu)解，平均絕對(duì)百分比誤差約13.92%，決定系數(shù)2約為?0.83，最大誤差約48.52%。

本文提出一種基于3參數(shù)理論模型的半經(jīng)驗(yàn)修正模型，先計(jì)算實(shí)際測(cè)量值與3參數(shù)理論模型估測(cè)值之間的誤差，再通過經(jīng)驗(yàn)方法枚舉出關(guān)于排量比的變化函數(shù)（作為不同類型的自變量）并進(jìn)行相關(guān)系數(shù)分析，優(yōu)選出相關(guān)系數(shù)最高的自變量并作為原理論模型的新增誤差補(bǔ)償項(xiàng)，進(jìn)而形成4參數(shù)半經(jīng)驗(yàn)?zāi)Ｐ?，其次?jì)算實(shí)際測(cè)量值與4參數(shù)半經(jīng)驗(yàn)?zāi)Ｐ凸罍y(cè)值之間的誤差，再通過經(jīng)驗(yàn)方法枚舉出關(guān)于負(fù)載轉(zhuǎn)矩的變化函數(shù)（作為不同類型的自變量）并進(jìn)行相關(guān)系數(shù)分析，優(yōu)選出相關(guān)系數(shù)最高的自變量并作為原理論模型的新增誤差補(bǔ)償項(xiàng)，進(jìn)而形成5參數(shù)半經(jīng)驗(yàn)?zāi)Ｐ?。改進(jìn)半經(jīng)驗(yàn)修正模型建立方法流程見圖9。

圖9 效率特性半經(jīng)驗(yàn)修正模型構(gòu)建流程

本文研究以排量比和負(fù)載轉(zhuǎn)矩的冪函數(shù)（指數(shù)冪分別為1～3）、ln函數(shù)、exp函數(shù)和三角函數(shù)（sin、cos、tan）作為相關(guān)系數(shù)分析的自變量。原理論模型、3參數(shù)理論模型、4參數(shù)半經(jīng)驗(yàn)修正模型和5參數(shù)半經(jīng)驗(yàn)修正模型的辨識(shí)精度對(duì)比見表1。

表1 不同模型辨識(shí)精度對(duì)比

由表1可知，本文提出的半經(jīng)驗(yàn)?zāi)Ｐ托拚椒ǚ?階段（階段1形成4參數(shù)半經(jīng)驗(yàn)修正模型，階段2形成5參數(shù)半經(jīng)驗(yàn)修正模型）進(jìn)行持續(xù)性優(yōu)化修正，第1階段引入關(guān)于排量比的相關(guān)函數(shù)，較原3參數(shù)理論模型平均絕對(duì)百分比誤差降低64.08%，決定系數(shù)提高183.13%；第2階段引入關(guān)于負(fù)載轉(zhuǎn)矩的相關(guān)函數(shù)，較第1階段修正模型（即4參數(shù)半經(jīng)驗(yàn)修正模型）平均絕對(duì)百分比誤差進(jìn)一步降低50.00%，決定系數(shù)進(jìn)一步提高34.78%。

5參數(shù)半經(jīng)驗(yàn)修正模型較原理論模型的平均絕對(duì)百分比誤差降低47.48%，決定系數(shù)提高32.86%。

5參數(shù)半經(jīng)驗(yàn)修正模型的辨識(shí)過程見圖10，其中外層循環(huán)200次的I-SA算法結(jié)果見圖10a，第138次外層循環(huán)計(jì)算結(jié)果最優(yōu)，內(nèi)層循環(huán)（即I-SA算法）的迭代過程見圖10b，根據(jù)最優(yōu)解建立的液壓傳動(dòng)系統(tǒng)效率特性模型計(jì)算結(jié)果見圖10c。

綜合對(duì)比圖8c和圖10c，修正后半經(jīng)驗(yàn)?zāi)Ｐ驮诠罍y(cè)精度以及液壓傳動(dòng)系統(tǒng)效率特性變化規(guī)律的描述和解釋上有明顯提高。本文研究對(duì)象的效率特性在大排量和大負(fù)載工況下具有較大值，并往中小排量和中小負(fù)載工況呈梯度性非線性逐步下降。修正后模型對(duì)于小排量（排量比為0.25）工況下效率特性變化依舊有著高度吻合的解釋，而原理論模型解釋性差。

圖10 效率特性的5參數(shù)修正模型參數(shù)辨識(shí)結(jié)果

5 結(jié) 論

1）基于液壓傳動(dòng)系統(tǒng)調(diào)速特性臺(tái)架試驗(yàn)樣本數(shù)據(jù)，調(diào)速特性除與排量比有明顯關(guān)系外，還主要受負(fù)載轉(zhuǎn)矩的影響。修正后液壓傳動(dòng)系統(tǒng)調(diào)速特性模型應(yīng)為原理論模型與負(fù)載扭矩1階線性模型的乘積組合，修正后模型精度提升明顯，提高34.41%。

2）基于液壓傳動(dòng)系統(tǒng)效率特性臺(tái)架試驗(yàn)樣本數(shù)據(jù)，效率特性主要與排量比和負(fù)載轉(zhuǎn)矩有關(guān)。本文提出的改進(jìn)半經(jīng)驗(yàn)修正模型建立方法有效修正了原理論模型，所建立的5參數(shù)半經(jīng)驗(yàn)修正模型的平均絕對(duì)百分比誤差較原理論模型降低47.48%，決定系數(shù)2達(dá)到0.93（提升32.86%），模型表征規(guī)律與實(shí)際測(cè)量值高度吻合，即在大排量和大負(fù)載工況下具有較大值，并往中小排量和中小負(fù)載工況呈梯度性非線性逐步下降，降幅逐步增加。

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Model modification and parameter identification of tractor hydraulic transmission system characteristics

Cheng Zhun1, Lu Zhixiong2

(1.,,210037,;2.,,210031,)

An accurate identification of a continuously variable transmission (CVT) system can greatly contribute to the tractor power device and the control strategy, particularly to the energy saving and emission reduction for the power improvement. This study aims to improve the accuracy of the theoretical model, due to the variation of the characteristics for the common continuously variable speed system with the working conditions. Taking hydrostatic transmission (HST) and hydro-mechanical continuously variable transmission (HMCVT) as the research objects, the speed regulation and efficiency characteristics of the hydraulic transmission system were determined under the working conditions (including engine speed, output load torque, and displacement ratio). The full-factor test was adopted to comprehensively analyze the hydraulic transmission system characteristics. Among them, the engine speed, output load torque, and displacement ratio were set at the 3-, 11-, and 5-levels, respectively. The samples of hydraulic transmission system characteristics were obtained by the bench test (including the test sample data of speed regulation characteristics and efficiency characteristics). The test bench was mainly composed of the variable pump, constant motor, diesel engine, wet clutch, several groups of gear devices and transmission shafts, as well as the speed torque sensors and the load device. Before that, the basic performance of the test bench was tested by the variable pump displacement ratio adjustment test (Test 1) and wet clutch test (Test 2). The influence degree of working conditions was compared using the partial least squares (PLS) method. Furthermore, the parameter identification and model correction of the hydraulic transmission system characteristics were proposed to combine the original theoretical model with the improved simulated annealing (I-SA). The simulated annealing was used as the inner cycle to construct the outer cycle. The disturbance number of the simulated annealing was improved to introduce an adaptive variation function. The results show that the speed regulation characteristics were closely related to the displacement ratio, depending mainly on the load torque, according to the bench test data from the hydraulic transmission system. PLS analysis showed that the influence degrees of the engine speed and output load torque (absolute value) were 0.36 and 0.92, respectively. The revised characteristics model of hydraulic transmission system speed regulation was the optimal combination of the original theoretical model and the first-order linear model of load torque. The accuracy of the revised model was significantly improved (34.41%) than before. The efficiency characteristics were mainly related to the displacement ratio and load torque, according to the bench test data of efficiency characteristics for the hydraulic transmission system. Among them, the influence degrees (absolute value) of the engine speed, output load torque, and displacement ratio were 0.05, 0.71, and 0.26, respectively. There was the limited accuracy of the original 6-parameter theoretical model (the mean absolute percentage error about 4.76%, and2about 0.70) after parameter identification, indicating the different overall change from the actual measurement. By contrast, the new semi-empirical modified model can be expected to effectively modify the original theoretical model. The mean absolute percentage error of the newly-developed 5-parameter semi-empirical modified model was improved by 47.48% than before, where the2was 0.93 (improved by 32.86%). The characterization of the new model was highly consistent with the actual measured values. Specifically, there was a large value in the conditions of large displacement and large load, indicating a divergent decline in the conditions of medium or small displacement and load, i.e., the gradually increased decline. Therefore, the I-SA algorithm can be expected to effectively serve as the engineering practice by introducing the outer cycle and the adaptive change of disturbance number. The reasonable design and control strategy can then be achieved in the correct speed regulation and efficiency characteristics model for the better performance of the tractor CVT system.

tractor; CVT; speed regulation characteristics; efficiency characteristics; parameter identification; semi-empirical model

10.11975/j.issn.1002-6819.2022.19.004

S232.3

A

1002-6819(2022)-19-0033-08

程準(zhǔn)，魯植雄. 拖拉機(jī)液壓傳動(dòng)系統(tǒng)特性模型修正與參數(shù)辨識(shí)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2022，38(19)：33-41.doi：10.11975/j.issn.1002-6819.2022.19.004 http://www.tcsae.org

Cheng Zhun, Lu Zhixiong. Model modification and parameter identification of tractor hydraulic transmission system characteristics[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2022, 38(19): 33-41. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2022.19.004 http://www.tcsae.org

2022-04-26

2022-06-21

國家自然科學(xué)基金項(xiàng)目（52105063）

程準(zhǔn)，博士，研究方向?yàn)檐囕v系統(tǒng)動(dòng)力學(xué)與控制、農(nóng)業(yè)機(jī)械裝備。Email：chengzhun38@163.com